I don’t see it as an argument against souls, myself. In theory we could have etherial cables plugged into our brains and sharing part of the processing work with the Big Computer In The Sky. Of course if this was the case mind and personality altering physical drugs would have no effect on the etherial portion and it would be impossible to do rare anomolous things like ‘get drunk from beer’. But that’s a separate argument: the mere fact that souls would need to function in a complex manner too isn’t an argument against their existing.
Personally I see no reason to distinguish between conscious and subconscious mind in this discussion: we have a mind, it processes data, it changes between states based on rules that are quite clearly not entirely random. That’s all we need to know.
As for whether we have free will or merely an illusion of it - wouldn’t it be helpful to define it first? Because in all honesty, aside from the “I’m completely unpredictable” part, we actually have most of what goes into free will: our thought processes are self-contained and relatively independent of outside influence, and they do make the choices that drive our lives. (See below.)
Choice only assumes that you have “free will” in the sense that your decisions are based on internal machinations and are not (completely) imposed externally. Thus, people make choices, computers make choices, anything that does internal calculation or deliberation prior to taking one action of several possibilities makes a choice. That’s how the word is used in english, pretty much whether you choose to like it or not.
And I’ll never understand the kind of thinking that says, “If my thoughts are deterministic, then it suddenly becomes rational to determine that the best way to act is one that will subject me to physical pain.” Why should realizing that your decisions are not made independently of your mind lead you to conclude that pain is suddenly a good thing?
Remember, this whole determinism thing isn’t taking your mind out of the equation. Your mind is part of the equation: the part that makes the choices as to what you do. That’s kinda what your mind is for - directing how your body reacts to its environment in order to be able to avoid danger, find safety, and purchase lattes. Mainly purchasing lattes. You’re a walking, talking, latte purchasing machine, and everything you think and learn and remember is done to hone your ability to react to your environment and better achieve your goals - which is to say, to purchase more lattes.
That being the case, what part of realizing that your mind is there to guide you towards satisfying it’s preferences (lattes!), what part of realizing that makes sabotaging yourself the better course to choose? Supposing you meet a god, and he offers you the choice: have a latte, or die. What is the line of thinking that is inexorably leading you to the conclusion that you should ask for death?
Because if you have such a line of thinking operating foremost in your head, then that’s what you’ll do: lines of thinking are how our brain calculates how to choose to act. That’s the determinism part. But this only happens if there’s a line of thought that deterministically leads to the conclusion, so for the love of all that’s caffinated, why on earth do you think asking to die would be a good idea?
Omnipotence is about what you could do. Omnibenevolence is what you would do. The actions a god (or anyone) take is always selected from the intersection of these two sets. This isn’t really a conflict, for most usual definitions of choice.
Faith is merely an abrogation of thought on the subject - it’s not a counter to a proof so much as a refusal to think about the subject. Admittedly, it’s usually pretty easy not to find it necessary to think about the subject, but that isn’t a strike against the proof, it’s a strike against the person refusing to think about it logically.
So it’s okay to recognize that no proof can convince the wilfully ignorant; of course it won’t. But then not accepting the logic of the proof yourself just because the theists won’t is kind of like jumping off the cliff because everyone else is doing it.
Just sayin’.
An omnimax god is not limited to only using Big Bangs as creation methods. Alternatively he could just pop the universe into existence in incremental steps over the course of a week, eschewing evolution entirely and just molding every living thing out of clay. Or he could just snap his fingers and pop the entire universe into being with the exact world-state as our universe was in last thursday, right down to our mental states containing false memories of the past. All these are possible for any god that is even vaguely close to omnimax. In fact, as can be seen from the example of last thursdayism, an omnimax god can create the universe directly into any logically-possible state, without having to shuttle it through any prior steps beforehand to reach that point, because having to go through prior steps is a logically unnecessary limitation on the power of the god.
So: The universe has a set of logically possible optimal states, and Omnimax God could (and would) ensure that the universe both started in and stayed in that set of states. If that required constant intervention on his part, so be it - he has the ability and will to do so. If he lacks the ability or will, then he’s not omnimax.
Also: how would evolution be an explanation of the Problem of Suffering? Letting the weak die (very likely while suffering) is an intrinsic part of evolution.
Also: When you start talking about being “worthy of worship”, you lose me, since worship strikes me as an inherently bad idea for both worshipper and worshipee, unless the entity demanding worship will lash out with punishment when they don’t get it, in which case they’re obviously not worthy. So the set of gods that should be worshipped is distinct and non-overlapping with the ones that are ‘worthy’ of it. (Assuming any are.)
If we’re random, then determinism is not true. And volition is necessarily a process: a mainly deterministic process, if we’re not random. There cannot possible be atomic “volition particles” that individually handle the process of accumulating, storing, analizing, and acting on the full body of knowledge and information that goes into human or godly decision making.
It’s tivially easy to define a logically possible universe that doesn’t have evil in it, for any non-logically-impossible definition of “good”. That is, if good itself is not logically impossible, then a universe could be created that exactly meets the definition. This is true by definition.
And you are grotesquely overblowing the limits implied by logical possibility. There is a rather wide chasm between “lacks square circles” and “necessarily contains evil”, unless you define evil as the lack of square circles. Failing that you are just saying “Are square circles possible? No? Then it’s probably logically impossible for it to snow in the winter, too. One thing being logical impossible means anything probably is.”
Obviously, this is not particularly compelling logic.
Especially since the empty universe and universes containing only the benevolent god are certainly logically possible (again, assuming that benevolent gods themselves aren’t logically impossible, which is necessary for your position in the argument). These theoretical worlds being possible definitively prove that evil is not necessary. (And no, accessibility doesn’t matter here.)

But I get there on evidential rather than logical grounds, which is why I think it’s not germaine to the OP. As I said earlier, the OP seems to be arguing that, epistemologically, we can’t be certain God can intervene without making the situation worse overall. (Actually, HMHW makes the argument in the context of creation, but it applies to the intervention problem as well.) As I also said, this may even be true (or not), but I don’t care. As a materialist, I work probabilities, not certainties. Again, taking me out of the OP. ISTM you want to argue the logical problem and the creation problem. That’s fine and what the OP is about. Carry on.